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## #1 2013-06-05 07:23:55

golchhamohit
Member
Registered: 2013-06-05
Posts: 10

### Black and White Hats

Hi,

I m new to this forum.I would like to get to know answer for this puzzle.

Cannibals ambush a safari in the jungle and capture three men. The cannibals give the men a single chance to escape uneaten.

The captives are lined up in order of height, and are tied to stakes. The man in the rear can see the backs of his two friends, the man in the middle can see the back of the man in front, and the man in front cannot see anyone. The cannibals show the men five hats. Three of the hats are black and two of the hats are white.

Blindfolds are then placed over each man's eyes and a hat is placed on each man's head. The two hats left over are hidden. The blindfolds are then removed and it is said to the men that if one of them can guess what color hat he is wearing they can all leave unharmed.

The man in the rear who can see both of his friends' hats but not his own says, "I don't know". The middle man who can see the hat of the man in front, but not his own says, "I don't know". The front man who cannot see ANYBODY'S hat says "I know!"

How did he know the color of his hat and what color was it?

I know the solution but not able to derive it.So a little help would be nice.Solution is given in home site itself.

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## #2 2013-06-05 17:17:52

{7/3}
Member
Registered: 2013-02-11
Posts: 210

### Re: Black and White Hats

Hi,golchhanmohit,this is a famous riddle,i derived the answer like this-if the guy in the back saw 2 white hat he would know what his hat was. Knowing this fact if the guy in the middle saw a white hat he would know what his hat was.since both of them didn't know what their hat was the hat in the front must be black.

Last edited by {7/3} (2013-06-05 17:20:56)

There are 10 kinds of people in the world,people who understand binary and people who don't.

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## #3 2013-06-05 18:55:58

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Black and White Hats

hi  golchhamohit

Welcome to the forum.

A concise solution from {7/3}.  Excellent!

This has come up before and been discussed at length.  You can check it out at

http://www.mathisfunforum.com/viewtopic.php?id=16065

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #4 2013-06-06 02:25:45

golchhamohit
Member
Registered: 2013-06-05
Posts: 10

### Re: Black and White Hats

thanks a lot {7/3} and bob bundy
I got my way

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## #5 2014-07-12 08:31:19

Fullerene
Member
Registered: 2014-07-12
Posts: 6

### Re: Black and White Hats

This solution is the logical approach to a sequencial display: each candidate can only regard who is in front of him and the solution is found from the information he gets from precedent speaker. A rather different situation is when the three candidates are placed in triangle and each one can see what colour have the hats of  the two other competitors, but not the colour of his hat. In that case two alternatives only exist and are immediate: or all the three cannot conclude or one and only one of them seeing two white hats in the others heads  immediately concludes that he has a black hat - with no need of logical reasoning at all!

Last edited by Fullerene (2014-07-12 08:38:39)

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## #6 2014-07-12 08:51:17

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Black and White Hats

True, but the problem in post #1 says they are placed one behind the other, so {7/3}'s solution applies there.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #7 2014-07-12 09:48:55

Fullerene
Member
Registered: 2014-07-12
Posts: 6

### Re: Black and White Hats

Not at all questioning  the solution of (7/3)'. Only giving an hint about a variation of the hats puzzle, that normally is not presented or discussed  because much more obvious.

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